應用馬氏距離於田口動態系統中等級類別資料最佳化問題

Abstract

在品質特性中僅能以優、劣等級劃分其類別者則稱為等級類別型品質性。然而在等級類別型資料中，區分類別有時會因為無精確的測量儀器及方法或基於成本的考量而必須採用人為主觀的方式來區分類別。工程人員可能因對缺陷認知的不同而有判斷上的差異，這種差異可能會造成在兩個相鄰的等級類別間出現判別的模糊地帶，這些模糊地帶的資料會造成類別間有某種相關性的存在，使得這些無法測量的品質特性所隱含的資訊不能充分地表現出來。此外，在製程參數最佳化的方面，田口品質工程可說是目前業界最常使用的方法。田口(Taguchi) 建議使用累積分析法(accumulation analysis)對等級類別資料的參數作最佳化分析，但有許多學者認為此法不夠完備，且其適用情況也僅限於靜態問題。而目前業界使用參數最佳化法於動態系統中的情況日益增多，因此本研究之目的是利用馬氏距離(Mahalnobis Distance)來解決類別間相關性的問題，衡量輸出值與目標值間的差異。以建立一套合理而有效動態系統等級類別參數最佳化的流程，最後並以一積體電路(Integrated Circuit)之電鍍均勻度(uniformity of plating)的製程參數最佳化實例來驗證本研究所提之參數最佳化的可行性及有效性。

Due to the increasing complexity of the product design, the quality response is often measured with ordered categorical scale by engineer’s subjective judgement when using design of experiments for quality improvement. The data among the ordered categories always exist some correlations because of subjective determining the ordered categories for quality response. Most of the existing optimization methods for order categorical response were for state system, methods for optimizing dynamic ordered categorical response are rarely seen. The accumulation analysis (AA), developed by Taguchi, can resolve a state ordered categorical response problem. However, Taguchi’s AA might lead to an erroneous result, because this method can measure location effect only and cannot reflect the dispersion effect. Therefore, this study develops a procedure using Mahalanobis distance which considers the correlation among categories. The proposed procedure is capable of optimizing dynamic categorical responses and simultaneously considering the location and dispersion effects. Therefore, it can explicitly depict the dynamic categorical response performances and accurately determine an optimal factor/level combination. Finally, a case study involving optimizing the uniformity of plating from an integrated circuit manufacturer, demonstrates the effectiveness of the proposed procedure.